# Breaking Down the Binomial Model to Value an Option ## Two period binomial option pricing model examples

You have an American call option expiring in 7-years with exercise price of \$85 on a stock which currently trades at \$89. You expect the stock to increase by a factor of and decrease by a factor of . If the interest rate is 8%, determine the option value.

## Two-State Option Pricing Model - University at Albany

The price of the underlying and the pay-off of the call option , at the end of Year 7, in case of up movement in both Year 6 and Year 7, equals \$ (=\$89 × × ) and \$ (\$ - \$85) respectively.

### Two Period Binomial Option Pricing Model - Breaking Down

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#### Lecture : Option Pricing Models: The Binomial Model

Forgive me my professor can have many errors in his problems. I am not sure how to solve this problem and what ATM call option mean. We have never covered dividends in regards to binomial model. I need some help with this any suggestions is greatly appreciated.

##### Binomial Option Calculator

The call option value using the one-period binomial model can be worked out using the following formula:

###### The 2-period Binomial Model

It is different from the Black-Scholes-Merton model which is most appropriate for valuing path-independent options.

I did the calculations, and actually both current answers seem wrong. can someone confirm or point towards any mistake in the following reasoning?

Binomial model is best represented using binomial trees which are diagrams that show option payoff and value at different nodes in the option’s life. The following binomial tree represents the general one-period call option.

The payoff pattern of a put option , an option that entitles the holder to sell the underlying at the exercise price is exactly opposite, . its value in case of an up (p + ) or down movement (p - ) in the underlying price S is max(X-uS,5) and max(X-dS,5) respectively. The value of a put option using single-period binomial model can be calculated using the following formula:

Where r is the risk-free rate , u equals the ratio the underlying price in case of an up move to the current price of the underlying and d equals the ratio of the underlying price in case of a down move to the current price of the underlying.

Using these final pay-offs, we can find out the call option value at the end of Year 6. In case of an upward movement in Year 6, there is a probability of that the option will be worth \$ (corresponding to underlying value of \$) and a probability of that it will be 5 (corresponding to underlying value of \$) at the end of Year 7. This information can be used to find out the option value at the end of Year 6: